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From: RRogers <rerogers@plaidheron.com>
Newsgroups: sci.stat.math,comp.soft-sys.matlab,sci.engr.control
Subject: Re: Kalman filtering with multiplicative noise
Date: Mon, 21 Jul 2008 07:41:29 -0700 (PDT)
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On Jul 20, 10:51 pm, d...@myallit.com wrote:
> I'm trying to implement a Kalman filter in MATLAB that will use two
> types of measurements: volume and in/out flow rate. For the flow rate,
> the measurement error is additive Gaussian, but for the volume the
> measurement error is expressed as a percentage of the volume, so that
> the volume measurement is less accurate when its value is higher. I
> think the measurement model should therefore be:
>
> Flow rate measurement model:
> z1 = x1 + v1 where v1 ~ N(0,e1)
>
> Volume measurement model:
> z2 = x2*v2 where v2 ~ N(1,e2)
>
> I assumed the volume filtering should be done in the log domain to
> make the noise additive but how do I deal with a noise mean of one
> when the Kalman filter assumes a mean of zero? And how can I have a
> Kalman filter using both the measurements if one is in the log domain
> and the other one isn't?
>
> I am also dealing with a system where measurements will usually be
> missing (they are arriving sequentially) and at an uneven sampling
> rate, any other pointers on these too would be appreciated.

Concerning the uneven sampling there have been discussions of this on
this newsgroup in the past; which I haven't followed carefully.
In my experience the uneven sampling could be rolled into either
multiplicative or additive noise and dealt with as another noise term;
but I had enough design freedom so that I could make do with these
approximations.   That is to say, the signals were always "chopped" to
avoid 1/f noise and actual information was contained in small
attenuation of the signals; thus the effect of the changing sampling
point could be estimated/bounded  by the chopped signal independent of
the information.

RayR

Ray